## Tamil Nadu Board of Secondary Education Class 11 Mathematics Syllabus - Free PDF Download

Tamil Nadu Board of Secondary Education Syllabus 2023-24 Class 11: The Tamil Nadu Board of Secondary Education Class 11 Mathematics Syllabus for the examination year 2023-24 has been released by the , Tamil Nadu Board of Secondary Education. The board will hold the final examination at the end of the year following the annual assessment scheme, which has led to the release of the syllabus. The 2023-24 Tamil Nadu Board of Secondary Education Class 11 Mathematics Board Exam will entirely be based on the most recent syllabus. Therefore, students must thoroughly understand the new Tamil Nadu Board of Secondary Education syllabus to prepare for their annual exam properly.

The detailed Tamil Nadu Board of Secondary Education Class 11 Mathematics Syllabus for 2023-24 is below.

## Tamil Nadu Board of Secondary Education Class 11 Mathematics Revised Syllabus

Tamil Nadu Board of Secondary Education Class 11 Mathematics and their Unit wise marks distribution

### Tamil Nadu Board of Secondary Education Class 11 Mathematics Course Structure 2023-24 With Marking Scheme

## Syllabus

- Introduction to Sets, Relations and Functions
- Sets
- Properties of Set Operations

- Cartesian Product
- Constants and Variables, Intervals and Neighbourhoods
- Constants and Variables
- Intervals and Neighbourhoods

- Type of Intervals
- Neighbourhood

- Concept of Relation
- Definition of Relation
- Domain
- Co-domain and Range of a Relation

- Functions
- Ways of Representing Functions

- Tabular Representation of a Function
- Graphical Representation of a Function
- Analytical Representation of a Function

- Some Elementary Functions
- Types of Functions
- Operations on Functions
- Inverse of a Function
- Algebra of Functions
- Some Special Functions

- Graphing Functions Using Transformations
- Type of Transformations

- Reflection
- Translation
- Dilations

- Introduction to Basic Algebra
- Real Number System
- Rational Numbers
- The Number Line
- Irrational Numbers
- Properties of Real Numbers

- Absolute Value
- Definition and Properties
- Equations Involving Absolute Value
- Some Results For Absolute Value
- Inequalities Involving Absolute Value

- Linear Inequalities
- Quadratic Functions
Given `alpha`,`beta` as roots then find the equation whose roots are of the form `alpha^3`, `beta^3` , etc

Case I:a>0 -> 1)Real roots, 2)Complex roots,3)Equal roots

Case II:a<0 -> 1)Real roots, 2)Complex roots,3)Equal roots

Where ‘a’ is the coefficient of x

^{2}in the equations of the form ax^{2}+ bx + c = 0.Understanding the fact that a quadratic expression (when plotted on a graph) is a parabola.

- Quadratic Formula
- Quadratic Inequalities

- Steps to Solve Quadratic Inequalities

- Polynomial Functions
- Division Algorithm
- Important Identities

- Rational Functions
- Rational Inequalities
- Partial Fractions
- Graphical Representation of Linear Inequalities

- Exponents and Radicals
- Exponents

- Properties of Exponents

- Radicals
- Exponential Function

- Properties of Exponential Function
- A Special Exponential Function

- Logarithms
- Properties of Logarithm

- Application of Algebra in Real Life

- Introduction of Trigonometry
- A Recall of Basic Results
- Angles
- Different Systems of measurement of angle
- Degree Measure
- Angles in Standard Position
- Coterminal angles
- Basic Trigonometric ratios using a right triangle
- Exact values of trigonometric functions of widely used angles
- Basic Trigonometric Identities

- Radian Measure
- Relationship between Degree and Radian Measures

- Trigonometric Functions and Their Properties
- Trigonometric Functions of any angle in terms of Cartesian coordinates

- Trigonometric ratios of Quadrantal angles

- Trigonometric Functions of real numbers

- Signs of Trigonometric functions

- Allied Angles
- Some Characteristics of Trigonometric Functions

- Periodicity of Trigonometric Functions
- Odd and Even trigonometric functions

- Trigonometric Identities

- Sum and difference identities or compound angles formulas
- Multiple angle identities and submultiple angle identities
- Conditional Trigonometric Identities

- Trigonometric Equations
- Properties of Triangle
- The Law of Sines or Sine Formula

- Law of Sines
- Law of Cosines
- Projection Formula
- Projection Formula
- Half-Angle formula

- Area of a triangle (Heron’s Formula )

- Application to Triangle
- Inverse Trigonometric Functions
- Introduction of Inverse Trigonometric Functions

- Combinatorics and Mathematical Induction
- Fundamental Principles of Counting
- Tree Diagram
- Addition Principle
- Multiplication principle

- Factorials
- Permutations
- Permutation
- Permutation of repeated things
- Permutations when all the objects are not distinct
- Number of Permutations Under Certain Restricted Conditions
- Circular Permutations

- Combinations
- Properties of Combinations

- Mathematical Induction

- Introduction to Binomial Theorem, Sequences and Series
- Binomial Theorem
- Binomial Coefficients
- Binomial theorem for positive integral inde

- Particular Cases of Binomial Theorem

- Finite Sequences
- Arithmetic and Geometric Progressions
- Arithmetico-Geometric Progression (AGP)
- Harmonic Progression (HP)

- Finite Series
- Sum of Arithmetic, Geometric and Arithmetico-Geometric Progressions
- Telescopic Summation for Finite Series
- Some Special Finite Series

- Infinite Sequences and Series
- Fibonacci Sequence
- Infinite Geometric Series
- Infinite Arithmetico-Geometric Series
- Telescopic Summation for Infinite Series
- Binomial Series
- Exponential Series
- Logarithmic Series

- Introduction to Two Dimensional Analytical Geometry
- Locus of a Point
- Procedure for finding the equation of the locus of a point

- Straight Lines
- Inclination of a line
- Slope of a line
- Perpendicular Lines
- Angle between intersecting lines
- Different Forms of an equation of a straight line
- General form to other forms

- Angle Between Two Straight Lines
- Condition for Parallel Lines
- Condition for perpendicular Lines
- Position of a point with respect to a straight line
- Distance Formulas
- Family of lines
- One parameter families
- Two parameters families
- The family of equation of straight lines through the point of intersection of the two givenlines

- Pair of Straight Lines
3.3.1 Combined equation of the pair of straight lines

3.3.2 Pair of straight lines passing through the origin

3.3.3 Angle between pair of straight lines passing through the origin

3.3.4 The condition for general second degree equation to represent the pair of straight

lines

- Equation of the bisectors of the angle between the lines
- General form of Pair of Straight Lines

- Introduction to Matrices and Determinants
- Matrices
- General form of a matrix
- Types of Matrices
- Equality of Matrices
- Algebraic Operations on Matrices
- Properties of Matrix Addition, Scalar Multiplication and Product of Matrices
- Operation of Transpose of a Matrix and its Properties
- Symmetric and Skew-symmetric Matrices

- Determinants
- Determinants of Matrices of different order
- Properties of Determinants
- Application of Factor Theorem to Determinants
- Product of Determinants
- Relation between a Determinant and its Cofactor Determinant
- Area of a Triangle
- Singular and non-singular Matrices

- Introduction to Vector Algebra
- Scalars and Vectors
- Scalars
- Vectors
- Position vector
- Displacement vector
- Resultant vector

- Representation of a Vector and Types of Vectors
- Algebra of Vectors
- Addition of Two Vectors

- Parallelogram Law

- Triangle Law of addition of two vectors - Subtraction of two vectors
- Scalar multiplication of a vector

- Addition of Two Vectors
- Position Vectors
- Resolution of Vectors
- Resolution of a vector in two dimension
- Resolution of a vector in three dimension
- Matrix representation of a vector

- Direction Cosines and Direction Ratios of a Line
- Relation between the direction cosines of a line
- Direction cosines of a line passing through two points
- Direction cosines/ratios of a line joining two points

- Product of Vectors
- Angle between two vectors
- Scalar product
- Properties of Scalar Product
- Vector Product
- Properties

- Introduction to Differential Calculus -limits and Continuity
- Concept of Limits
- Definition of Limit
- One-Sided Limit
- Left-hand Limit
- Right-hand Limit
- Existence of a limit of a function at a point x = a
- Algebra of limits:

Let f(x) and g(x) be two functions such that

`lim_(x→a) f(x) = l and lim_(x → a) g(x) = m, then`

1. `lim_(x → a) [f(x) ± g(x)] = lim_(x → a) f(x) ± lim_(x → a) g(x) = l ± m`

2. `lim_(x → a) [f(x) xx g(x)] = lim_(x→ a) f(x) xx lim_(x→ a) g(x) = l xx m`

3. `lim_(x → a) [kf(x)] = k xx lim_(x→ a) f(x) = kl, "where" ‘k’ "is a constant"`

4. `lim_(x → a) f(x)/g(x) = (lim_(x → a) f(x))/(lim_(x → a) g(x)) = l/m "where" m≠ 0`.

- Continuity
- Examples of functions Continuous at a point
- Algebra of continuous functions
- Removable and Jump Discontinuities

- Introduction of Differential Calculus-differentiability and Methods of Differentiation
- The Concept of Derivative
- The tangent line problem
- Velocity of Rectilinear motion
- The derivative of a Function
- One sided derivatives (left hand and right hand derivatives)

- Differentiability and Continuity
- Differentiation Rules
- Derivatives of basic elementary functions

- The derivative of a constant function is zero
- The power function y = xn, n > 0 is an integer
- Derivative of the logarithmic function
- Derivative of the exponential function
- The derivatives of the Trigonometric functions

- Examples on Chain Rule
- Implicit Differentiation
- Logarithmic Differentiation
- Substitution method
- Derivatives of variables defined by parametric equations
- Differentiation of one function with respect to another function
- Higher order Derivatives

- Integral Calculus
- Integration
- Meaning
- Basic Rule of Integration
- Application of Integration
- Consumer’s Surplus

- Newton-leibnitz Integral
- Basic Rules of Integration
- Integrals of the Form
- Properties of Integrals
- Simple Applications
- Indefinite Integration
- Methods of Integration
- Decomposition method
- Decomposition by Partial Fractions
- Method of substitution or change of variable
- Important Results
- Integration by parts
- Bernoulli’s formula for Integration by Parts
- Integrals of the form
- Integration of Rational Algebraic Functions

- Methods of Integration

- Introduction to Probability Theory
- Basic Definitions
- Finite Sample Space
- Types of events
- Methods to find sample space
- Notations

- Probability
- Basic concepts of Probability
- Independent and Dependent events
- Conditional Probability
- Baye’s Theorem
- Axiomatic approach to Probability
- ODDS

- Some Basic Theorems on Probability
- Conditional Probability
- Independent Events

- Total Probability of an Event
- Bayesâ€™ Theorem
- Partition of a sample space
- Theorem of total probability